Hierarchy of quantum explicitly solvable and integrable models

Details Hierarchy of quantum explicitly solvable and integrable models Hierarchy of quantum explicitly solvable and integrable models

2002-02-20

arxiv.org/abs/nlin/0202043v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, LaTeX, to be published in Theor. Math. Phys., added reference

Scientific paper

Realizing bosonic field v(x) as current of massless (chiral) fermions we derive hierarchy of quantum polynomial interactions of the field v(x) that are completely integrable and lead to linear evolutions for the fermionic field. It is proved that in the classical limit this hierarchy reduces to the dispersionless KdV hierarchy. Application of our construction to quantization of generic completely integrable interaction is demonstrated by example of the mKdV equation.

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